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带p-Laplacian算子的四点边值问题拟对称正解的存在性
引用本文:纪德红,田玉,葛渭高.带p-Laplacian算子的四点边值问题拟对称正解的存在性[J].数学的实践与认识,2008,38(19).
作者姓名:纪德红  田玉  葛渭高
基金项目:国家自然科学基金 , 教育部高等学校博士学科点专项科研基金 , 国家自然科学数学天元青年基金  
摘    要:利用范数形式的锥拉伸与压缩不动点定理,研究了一类p-Laplacian方程四点边值问题(φp(u′(t)))′(t)+λf(t,u(t))=0,t∈(0,1),u(0)-βu′(ξ)=0,u(ξ)-δu′(η)=u(1)+δu′(1+ξ-η),其中φp(s)=sp-2·s,p>1.获得了其拟对称正解的存在性定理.

关 键 词:拟对称正解  p-Laplacian算子  不动点定理  

Existence of Positive Pseudo——Symmetric Solutions to a Four-Point Boundary Value Problem with p-Laplacian
JI De-hong,TIAN Yu,GE Wei-gao.Existence of Positive Pseudo——Symmetric Solutions to a Four-Point Boundary Value Problem with p-Laplacian[J].Mathematics in Practice and Theory,2008,38(19).
Authors:JI De-hong  TIAN Yu  GE Wei-gao
Abstract:We considered the existence of positive pseudo-symmetric solutions for four-point boundary value problems of p-Laplacianequations (φp(u'))'(t)+λf(t,u(t))=0, t∈(0,1),u(0)-βu'(ξ)=0, u(ξ)-δu'(η)=u(1)+δu'(1+ξ-η).By using the fixed-point theorem of cone expansion-compression type with norm. Several sufficient conditions are established.
Keywords:positive pseudo-symmetric solution  p-Laplacianoperator  fixed point theorem  cone
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